Since I'm trying to understand why the electric field is null inside a charged conductor, and the explanation usually given is that "the charges rearrange themeselves in such a way as to nullify the electric field inside the conductor", what I need is an example of continuous charge distribution for which the electric field is null in a finite region.
If I consider the Poisson's equation inside a conductor, what I get by enforcing V = constant is that $\bigtriangleup V = 0$ and then $\rho=0$. So I'm confused
I would be happy to have an answer just for the case of a spherical region.
Or, you could provide a link to a mathematical proof for the existence of an equilibrium configuration for a set of charged particles constrained in a finite region